What is the solution for 10y^{''}+90y^'+140y=0,y(0)=0,y^'(0)=1 ?

The solution for 10y^{''}+90y^'+140y=0,y(0)=0,y^'(0)=1 is y= 1/5 e^{-2t}-1/5 e^{-7t}

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10y^{''}+90y^'+140y=0,y(0)=0,y^'(0)=1

10 y^{^{''}} + 90 y^{^{'}} + 140 y = 0, y (0) = 0, y^{^{'}} (0) = 1

y = \frac{1}{5} e^{- 2 t} - \frac{1}{5} e^{- 7 t}

Solution steps

10 y^{''} (t) + 90 y^{'} (t) + 140 y = 0

Solve linear ODE:

y = \frac{1}{5} e^{- 2 t} - \frac{1}{5} e^{- 7 t}

y = \frac{1}{5} e^{- 2 t} - \frac{1}{5} e^{- 7 t}

y^{^{''}} - 8 y^{^{'}} + 3 y = 0

\frac{d ^{2} x}{d t ^{2}} + 6 \frac{d x}{d t} + 9 x = 0

y^{^{'''}} + y^{^{'}} = 0, y^{^{'}} (0) = 1, y^{^{''}} (0) = 2

y^{^{''''}} + y^{^{''}} + 9 y = 0

y^{^{''}} - 7 y^{^{'}} + 10 y = 0, y (0) = 1, y^{^{'}} (0) = - 1

What is the solution for 10y^{''}+90y^'+140y=0,y(0)=0,y^'(0)=1 ?
The solution for 10y^{''}+90y^'+140y=0,y(0)=0,y^'(0)=1 is y= 1/5 e^{-2t}-1/5 e^{-7t}